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Rep. Jackie Speier, a Democrat who sits on the committee, said in a statement that her "fears have been validated" by the developments.
"Through his bizarre and partisan actions over the last week, Chairman Nunes has demonstrated to the entire nation why he is unfit to lead our critical investigation into ties between President Trump's administration and Moscow," she said.
After the meeting between Nunes and Trump last week, Trump said he felt "somewhat" vindicated about his unsupported claims that the Obama administration ordered a wiretapping operation on Trump Tower during the 2016 election.
Speier said the timing of Nunes' meeting on White House property, his revelations about information collected on Trump associates, and his briefing with the president are questionable.
"This implies that the Chairman and the White House colluded in a desperate attempt to salvage the President's credibility after the President's bogus wiretapping claims were debunked by his own FBI Director," Speier's statement read.
Speier continued: "In order to make sense of these developments, the White House must release its visitor logs so we can learn who from the President's staff granted the Chairman access to the White House complex and where he viewed the documents."
The congresswoman echoed growing calls for an independent investigation into Russia's alleged involvement in the US election.
The ranking Democrat on the committee, Rep. Adam Schiff of California, blasted Nunes for the move, saying it compromised their committee's investigation.
"At this point, the only people who do know are the chairman and the president," Schiff told NPR. "And given that the president's associates are the subject in part of the investigation, that's wholly inappropriate, and, unfortunately, I think it really impugns the credibility of the chairman in terms of his ability to conduct an independent investigation."
Schiff told reporters on Friday that Nunes had canceled an open House Intelligence Committee hearing set for this week with former Director of National Intelligence James Clapper, former CIA Director John Brennan, and former acting Attorney General Sally Yates.
Democratic Rep. Jim Himes, a member of the House Intelligence Committee, told CNN on Monday that the committee had been kept "totally out of the loop" on Nunes' actions and whereabouts.